The data on which philosophical theorizing is based are rather the intuited contents themselves, concerning the various thought experiments. At least that is so outside the epistemology of the a priori.
Philosophers need not much use the word 'intuition' or the concept of intuition, except when they happen to be working on the epistemology of the a priori.
Time is not an empirical concept. For neither co-existence nor succession would be perceived by us, if the representation of time did not exist as a foundation a priori.
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